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Intrinsic dimension identification via graph-theoretic methods

Author

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  • Brito, M.R.
  • Quiroz, A.J.
  • Yukich, J.E.

Abstract

Three graph theoretical statistics are considered for the problem of estimating the intrinsic dimension of a data set. The first is the “reach” statistic, r¯j,k, proposed in Brito et al. (2002) [4] for the problem of identification of Euclidean dimension. The second, Mn, is the sample average of squared degrees in the minimum spanning tree of the data, while the third statistic, Unk, is based on counting the number of common neighbors among the k-nearest, for each pair of sample points {Xi,Xj}, i

Suggested Citation

  • Brito, M.R. & Quiroz, A.J. & Yukich, J.E., 2013. "Intrinsic dimension identification via graph-theoretic methods," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 263-277.
    • Handle: RePEc:eee:jmvana:v:116:y:2013:i:c:p:263-277
    DOI: 10.1016/j.jmva.2012.12.007
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    References listed on IDEAS

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    1. Brito, María R. & Quiroz, Adolfo J. & Yukich, J. E., 2002. "Graph-Theoretic Procedures for Dimension Identification," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 67-84, April.
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    Cited by:

    1. S. Camelo & M. González-Lima & A. Quiroz, 2015. "Nearest neighbors methods for support vector machines," Annals of Operations Research, Springer, vol. 235(1), pages 85-101, December.
    2. Díaz, Mateo & Quiroz, Adolfo J. & Velasco, Mauricio, 2019. "Local angles and dimension estimation from data on manifolds," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 229-247.

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    1. S. Camelo & M. González-Lima & A. Quiroz, 2015. "Nearest neighbors methods for support vector machines," Annals of Operations Research, Springer, vol. 235(1), pages 85-101, December.
    2. Díaz, Mateo & Quiroz, Adolfo J. & Velasco, Mauricio, 2019. "Local angles and dimension estimation from data on manifolds," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 229-247.
    3. González-Barrios, José María & Quiroz, Adolfo J., 2003. "A clustering procedure based on the comparison between the k nearest neighbors graph and the minimal spanning tree," Statistics & Probability Letters, Elsevier, vol. 62(1), pages 23-34, March.

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